Analytic model for a frictional shallow-water undular bore

We use the integrable Kaup-Boussinesq shallow water system, modified by a small viscous term, to model the formation of an undular bore with a steady profile. The description is made in terms of the corresponding integrable Whitham system, also appropriately modified by friction. This is derived in Riemann variables using a modified finite-gap integration technique for the AKNS scheme. The Whitham system is then reduced to a simple first-order differential equation which is integrated numerically to obtain an asymptotic profile of the undular bore, with the local oscillatory structure described by the periodic solution of the unperturbed Kaup-Boussinesq system. This solution of the Whitham equations is shown to be consistent with certain jump conditions following directly from conservation laws for the original system. A comparison is made with the recently studied dissipationless case for the same system, where the undular bore is unsteady.Comment: 24 page

Phonon drag in ballistic quantum wires

The acoustic phonon-mediated drag-contribution to the drag current created in the ballistic transport regime in a one-dimensional nanowire by phonons generated by a current-carrying ballistic channel in a nearby nanowire is calculated. The threshold of the phonon-mediated drag current with respect to bias or gate voltage is predicted.Comment: 5 pages, 2 figure

Formation of shock waves in a Bose-Einstein condensate

We consider propagation of density wave packets in a Bose-Einstein condensate. We show that the shape of initially broad, laser-induced, density perturbation changes in the course of free time evolution so that a shock wave front finally forms. Our results are well beyond predictions of commonly used zero-amplitude approach, so they can be useful in extraction of a speed of sound from experimental data. We discuss a simple experimental setup for shock propagation and point out possible limitations of the mean-field approach for description of shock phenomena in a BEC.Comment: 8 pages & 6 figures, minor changes, more references, to appear in Phys. Rev.

Controlled nanochannel lattice formation utilizing prepatterned substrates

Solid substrates can be endued with self-organized regular stripe patterns of nanoscopic lengthscale by Langmuir-Blodgett transfer of organic monolayers. Here we consider the effect of periodically prepatterned substrates on this process of pattern formation. It leads to a time periodic forcing of the oscillatory behavior at the meniscus. Utilizing higher order synchronization with this forcing, complex periodic patterns of predefined wavelength can be created. The dependence of the synchronization on the amplitude and the wavelength of the wetting contrast is investigated in one and two spatial dimensions and the resulting patterns are discussed. Furthermore, the effect of prepatterned substrates on the pattern selection process is investigated

Runaway Quarks

When heavy nuclei collide, a quark-gluon plasma is formed. The plasma is subject to strong electric field due to the charge of the colliding nuclei. The electric field can influence the behavior of the quark-gluon plasma. In particular, we might observe an increased number of quarks moving in the direction of that field, as we do in the standard electron-ion plasma. In this paper we show that this phenomenon, called the runaway quarks, does not exist.Comment: 13 pages, uses harvmac.tex, epsf.te

Dynamics of a thin liquid film with surface rigidity and spontaneous curvature

The effect of rigid surfaces on the dynamics of thin liquid films which are amenable to the lubrication approximation is considered. It is shown that the Helfrich energy of the layer gives rise to additional terms in the time-evolution equations of the liquid film. The dynamics is found to depend on the absolute value of the spontaneous curvature, irrespective of its sign. Due to the additional terms, a novel finite wavelength instability of flat rigid interfaces can be observed. Furthermore, the dependence of the shape of a droplet on the bending rigidity as well as on the spontaneous curvature is discussed.Comment: 4 pages, 5 figure

Cavity solitons in vertical-cavity surface-emitting lasers

We investigate a control of the motion of localized structures of light by means of delay feedback in the transverse section of a broad area nonlinear optical system. The delayed feedback is found to induce a spontaneous motion of a solitary localized structure that is stationary and stable in the absence of feedback. We focus our analysis on an experimentally relevant system namely the Vertical-Cavity Surface-Emitting Laser (VCSEL). In the absence of the delay feedback we present experimental evidence of stationary localized structures in a 80 $\mu$m aperture VCSEL. The spontaneous formation of localized structures takes place above the lasing threshold and under optical injection. Then, we consider the effect of the time-delayed optical feedback and investigate analytically the role of the phase of the feedback and the carrier lifetime on the self-mobility properties of the localized structures. We show that these two parameters affect strongly the space time dynamics of two-dimensional localized structures. We derive an analytical formula for the threshold associated with drift instability of localized structures and a normal form equation describing the slow time evolution of the speed of the moving structure.Comment: 7 pages, 5 figure

Solitons of the Resonant Nonlinear Schrodinger Equation with Nontrivial Boundary Conditions and Hirota Bilinear Method

Physically relevant soliton solutions of the resonant nonlinear Schrodinger (RNLS) equation with nontrivial boundary conditions, recently proposed for description of uniaxial waves in a cold collisionless plasma, are considered in the Hirota bilinear approach. By the Madelung representation, the model is transformed to the reaction-diffusion analog of the NLS equation for which the bilinear representation, soliton solutions and their mutual interactions are studied.Comment: 15 pages, 1 figure, talk presented in Workshop `Nonlinear Physics IV: Theory and Experiment`, 22-30 June 2006, Gallipoli, Ital